TSTP Solution File: LCL800_5 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LCL800_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:31:49 EDT 2023
% Result : Theorem 6.21s 2.46s
% Output : Refutation 6.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 149
% Syntax : Number of formulae : 255 ( 136 unt; 45 typ; 0 def)
% Number of atoms : 416 ( 267 equ; 0 cnn)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 2070 ( 53 ~; 9 |; 43 &;1847 @)
% ( 20 <=>; 98 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 54 ( 54 >; 0 *; 0 +; 0 <<)
% Number of symbols : 46 ( 44 usr; 11 con; 0-5 aty)
% Number of variables : 535 ( 0 ^; 500 !; 8 ?; 535 :)
% ( 27 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(dB_type,type,
dB: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(zero_type,type,
zero:
!>[TA: $tType] : $o ).
thf(comm_monoid_add_type,type,
comm_monoid_add:
!>[TA: $tType] : $o ).
thf(ab_semigroup_add_type,type,
ab_semigroup_add:
!>[TA: $tType] : $o ).
thf(cancel_semigroup_add_type,type,
cancel_semigroup_add:
!>[TA: $tType] : $o ).
thf(cancel146912293up_add_type,type,
cancel146912293up_add:
!>[TA: $tType] : $o ).
thf(linord219039673up_add_type,type,
linord219039673up_add:
!>[TA: $tType] : $o ).
thf(plus_plus_type,type,
plus_plus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(zero_zero_type,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(equal_equal_type,type,
equal_equal:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(it_type,type,
it: dB > $o ).
thf(app_type,type,
app: dB > dB > dB ).
thf(var_type,type,
var: nat > dB ).
thf(dB_case_type,type,
dB_case:
!>[TA: $tType] : ( ( fun @ nat @ TA ) > ( fun @ dB @ ( fun @ dB @ TA ) ) > ( fun @ dB @ TA ) > dB > TA ) ).
thf(dB_rec_type,type,
dB_rec:
!>[TA: $tType] : ( ( fun @ nat @ TA ) > ( fun @ dB @ ( fun @ dB @ ( fun @ TA @ ( fun @ TA @ TA ) ) ) ) > ( fun @ dB @ ( fun @ TA @ TA ) ) > dB > TA ) ).
thf(dB_size_type,type,
dB_size: dB > nat ).
thf(lift_type,type,
lift: dB > nat > dB ).
thf(liftn_type,type,
liftn: nat > dB > nat > dB ).
thf(subst_type,type,
subst: dB > dB > nat > dB ).
thf(substn_type,type,
substn: dB > dB > nat > dB ).
thf(listMem_type,type,
listMem:
!>[TA: $tType] : ( TA > ( list @ TA ) > $o ) ).
thf(insert_type,type,
insert:
!>[TA: $tType] : ( TA > ( list @ TA ) > ( list @ TA ) ) ).
thf(cons_type,type,
cons:
!>[TA: $tType] : ( TA > ( list @ TA ) > ( list @ TA ) ) ).
thf(nil_type,type,
nil:
!>[TA: $tType] : ( list @ TA ) ).
thf(list_case_type,type,
list_case:
!>[TA: $tType,TB: $tType] : ( TB > ( fun @ TA @ ( fun @ ( list @ TA ) @ TB ) ) > ( list @ TA ) > TB ) ).
thf(list_rec_type,type,
list_rec:
!>[TA: $tType,TB: $tType] : ( TB > ( fun @ TA @ ( fun @ ( list @ TA ) @ ( fun @ TB @ TB ) ) ) > ( list @ TA ) > TB ) ).
thf(member1_type,type,
member1:
!>[TA: $tType] : ( ( list @ TA ) > TA > $o ) ).
thf(null_type,type,
null:
!>[TA: $tType] : ( ( list @ TA ) > $o ) ).
thf(splice_type,type,
splice:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) > ( list @ TA ) ) ).
thf(sublist_type,type,
sublist:
!>[TA: $tType] : ( ( list @ TA ) > ( fun @ nat @ bool ) > ( list @ TA ) ) ).
thf(suc_type,type,
suc: nat > nat ).
thf(size_size_type,type,
size_size:
!>[TA: $tType] : ( TA > nat ) ).
thf(aa_type,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ TA ) > TB > TA ) ).
thf(member_type,type,
member:
!>[TA: $tType] : ( TA > ( fun @ TA @ bool ) > $o ) ).
thf(pp_type,type,
pp: bool > $o ).
thf(a_type,type,
a: dB ).
thf(as_type,type,
as: list @ dB ).
thf(i_type,type,
i: nat ).
thf(n_type,type,
n: nat ).
thf(rs_type,type,
rs: list @ dB ).
thf(t_type,type,
t: dB ).
thf(u_type,type,
u: dB ).
thf(ua_type,type,
ua: dB ).
thf(34,axiom,
! [A: nat,B: nat] :
( ( ( plus_plus @ nat @ B @ A )
= B )
=> ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_add__eq__self__zero) ).
thf(234,plain,
! [A: nat,B: nat] :
( ( ( plus_plus @ nat @ B @ A )
= B )
=> ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(25,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( nil @ TA )
!= ( cons @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_list_Osimps_I2_J) ).
thf(184,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( nil @ TA )
!= ( cons @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(67,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ A @ B ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_add__right__cancel) ).
thf(371,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ A @ B ) )
=> ( C = A ) )
& ( ( C = A )
=> ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(90,axiom,
! [A: nat,B: dB,C: dB,D: nat] :
( ( liftn @ D @ ( app @ C @ B ) @ A )
= ( app @ ( liftn @ D @ C @ A ) @ ( liftn @ D @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_liftn_Osimps_I2_J) ).
thf(446,plain,
! [A: nat,B: dB,C: dB,D: nat] :
( ( liftn @ D @ ( app @ C @ B ) @ A )
= ( app @ ( liftn @ D @ C @ A ) @ ( liftn @ D @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(84,axiom,
! [A: dB,B: dB] :
( ( size_size @ dB @ ( app @ B @ A ) )
= ( plus_plus @ nat @ ( plus_plus @ nat @ ( size_size @ dB @ B ) @ ( size_size @ dB @ A ) ) @ ( suc @ ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_dB_Osize_I5_J) ).
thf(433,plain,
! [A: dB,B: dB] :
( ( size_size @ dB @ ( app @ B @ A ) )
= ( plus_plus @ nat @ ( plus_plus @ nat @ ( size_size @ dB @ B ) @ ( size_size @ dB @ A ) ) @ ( suc @ ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(66,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: TA] :
( ( listMem @ TA @ C @ B )
=> ( listMem @ TA @ C @ ( cons @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_insert) ).
thf(369,plain,
! [TA: $tType,A: TA,B: list @ TA,C: TA] :
( ( listMem @ TA @ C @ B )
=> ( listMem @ TA @ C @ ( cons @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(43,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_add_Ocomm__neutral) ).
thf(276,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(91,axiom,
! [TA: $tType,A: dB,B: dB,C: fun @ dB @ TA,D: fun @ dB @ ( fun @ dB @ TA ),E: fun @ nat @ TA] :
( ( dB_case @ TA @ E @ D @ C @ ( app @ B @ A ) )
= ( aa @ dB @ TA @ ( aa @ dB @ ( fun @ dB @ TA ) @ D @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_dB_Osimps_I11_J) ).
thf(449,plain,
! [TA: $tType,A: dB,B: dB,C: fun @ dB @ TA,D: fun @ dB @ ( fun @ dB @ TA ),E: fun @ nat @ TA] :
( ( dB_case @ TA @ E @ D @ C @ ( app @ B @ A ) )
= ( aa @ dB @ TA @ ( aa @ dB @ ( fun @ dB @ TA ) @ D @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(38,axiom,
! [A: nat] :
( ( size_size @ dB @ ( var @ A ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_dB_Osize_I4_J) ).
thf(247,plain,
! [A: nat] :
( ( size_size @ dB @ ( var @ A ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(12,axiom,
! [TA: $tType,A: list @ TA] :
( ( equal_equal @ ( list @ TA ) @ A @ ( nil @ TA ) )
<=> ( null @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_equal__Nil__null) ).
thf(142,plain,
! [TA: $tType,A: list @ TA] :
( ( ( equal_equal @ ( list @ TA ) @ A @ ( nil @ TA ) )
=> ( null @ TA @ A ) )
& ( ( null @ TA @ A )
=> ( equal_equal @ ( list @ TA ) @ A @ ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(97,axiom,
! [A: dB,B: dB] :
( ( dB_size @ ( app @ B @ A ) )
= ( plus_plus @ nat @ ( plus_plus @ nat @ ( dB_size @ B ) @ ( dB_size @ A ) ) @ ( suc @ ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_dB_Osize_I2_J) ).
thf(472,plain,
! [A: dB,B: dB] :
( ( dB_size @ ( app @ B @ A ) )
= ( plus_plus @ nat @ ( plus_plus @ nat @ ( dB_size @ B ) @ ( dB_size @ A ) ) @ ( suc @ ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(16,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_not0__implies__Suc) ).
thf(153,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(85,axiom,
it @ t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__096IT_At_096) ).
thf(436,plain,
it @ t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(41,axiom,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ ( suc @ B ) @ A )
= ( suc @ ( plus_plus @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_add__Suc) ).
thf(257,plain,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ ( suc @ B ) @ A )
= ( suc @ ( plus_plus @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(23,axiom,
! [A: nat,B: nat] :
( ( ( plus_plus @ nat @ B @ A )
= ( zero_zero @ nat ) )
<=> ( ( B
= ( zero_zero @ nat ) )
& ( A
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_add__is__0) ).
thf(174,plain,
! [A: nat,B: nat] :
( ( ( ( plus_plus @ nat @ B @ A )
= ( zero_zero @ nat ) )
=> ( ( B
= ( zero_zero @ nat ) )
& ( A
= ( zero_zero @ nat ) ) ) )
& ( ( ( B
= ( zero_zero @ nat ) )
& ( A
= ( zero_zero @ nat ) ) )
=> ( ( plus_plus @ nat @ B @ A )
= ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(76,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_zero__reorient) ).
thf(404,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( ( zero_zero @ TA )
= A )
=> ( A
= ( zero_zero @ TA ) ) )
& ( ( A
= ( zero_zero @ TA ) )
=> ( ( zero_zero @ TA )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(79,axiom,
! [A: nat] :
( ( suc @ A )
!= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_Suc__neq__Zero) ).
thf(416,plain,
! [A: nat] :
( ( suc @ A )
!= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(53,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( ( cons @ TA @ D @ C )
= ( cons @ TA @ B @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_list_Oinject) ).
thf(316,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( ( ( cons @ TA @ D @ C )
= ( cons @ TA @ B @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( cons @ TA @ D @ C )
= ( cons @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(98,axiom,
n = i,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_True) ).
thf(475,plain,
n = i,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(20,axiom,
! [A: nat] :
( ( suc @ A )
!= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_Suc__not__Zero) ).
thf(164,plain,
! [A: nat] :
( ( suc @ A )
!= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(40,axiom,
! [A: nat] :
( ( suc @ A )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_Suc__n__not__n) ).
thf(253,plain,
! [A: nat] :
( ( suc @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(102,axiom,
! [A: nat,B: dB,C: dB] :
( ( lift @ ( app @ C @ B ) @ A )
= ( app @ ( lift @ C @ A ) @ ( lift @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_lift_Osimps_I2_J) ).
thf(485,plain,
! [A: nat,B: dB,C: dB] :
( ( lift @ ( app @ C @ B ) @ A )
= ( app @ ( lift @ C @ A ) @ ( lift @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(1,conjecture,
it @ ( app @ u @ ( subst @ a @ u @ i ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( it @ ( app @ u @ ( subst @ a @ u @ i ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(106,plain,
~ ( it @ ( app @ u @ ( subst @ a @ u @ i ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(35,axiom,
! [A: nat] :
( ( plus_plus @ nat @ ( zero_zero @ nat ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_plus__nat_Oadd__0) ).
thf(238,plain,
! [A: nat] :
( ( plus_plus @ nat @ ( zero_zero @ nat ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(61,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ A @ B ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_nat__add__right__cancel) ).
thf(348,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ A @ B ) )
=> ( C = A ) )
& ( ( C = A )
=> ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(100,axiom,
! [A: dB,B: dB,C: nat] :
( ( var @ C )
!= ( app @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_dB_Osimps_I4_J) ).
thf(480,plain,
! [A: dB,B: dB,C: nat] :
( ( var @ C )
!= ( app @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(14,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( member @ TA @ B @ A )
<=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_mem__def) ).
thf(147,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( ( member @ TA @ B @ A )
=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) )
& ( ( pp @ ( aa @ TA @ bool @ A @ B ) )
=> ( member @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(74,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( cons @ TA @ B @ A )
!= ( nil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_list_Osimps_I3_J) ).
thf(397,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( cons @ TA @ B @ A )
!= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(10,axiom,
! [TA: $tType,A: list @ TA] :
( ( null @ TA @ A )
<=> ( A
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_List_Onull__def) ).
thf(133,plain,
! [TA: $tType,A: list @ TA] :
( ( ( null @ TA @ A )
=> ( A
= ( nil @ TA ) ) )
& ( ( A
= ( nil @ TA ) )
=> ( null @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(77,axiom,
cancel_semigroup_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__semigroup__add) ).
thf(411,plain,
cancel_semigroup_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(5,axiom,
! [TA: $tType] : ( null @ TA @ ( nil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_null__rec_I2_J) ).
thf(116,plain,
! [TA: $tType] : ( null @ TA @ ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(28,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( B
!= ( cons @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_not__Cons__self) ).
thf(206,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( B
!= ( cons @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(48,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus @ nat @ ( plus_plus @ nat @ C @ B ) @ A )
= ( plus_plus @ nat @ C @ ( plus_plus @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_nat__add__assoc) ).
thf(292,plain,
! [A: nat,B: nat,C: nat] :
( ( plus_plus @ nat @ ( plus_plus @ nat @ C @ B ) @ A )
= ( plus_plus @ nat @ C @ ( plus_plus @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(92,axiom,
! [TA: $tType,A: dB,B: dB,C: fun @ dB @ ( fun @ TA @ TA ),D: fun @ dB @ ( fun @ dB @ ( fun @ TA @ ( fun @ TA @ TA ) ) ),E: fun @ nat @ TA] :
( ( dB_rec @ TA @ E @ D @ C @ ( app @ B @ A ) )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( aa @ dB @ ( fun @ TA @ ( fun @ TA @ TA ) ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ TA @ ( fun @ TA @ TA ) ) ) @ D @ B ) @ A ) @ ( dB_rec @ TA @ E @ D @ C @ B ) ) @ ( dB_rec @ TA @ E @ D @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_dB_Orecs_I2_J) ).
thf(452,plain,
! [TA: $tType,A: dB,B: dB,C: fun @ dB @ ( fun @ TA @ TA ),D: fun @ dB @ ( fun @ dB @ ( fun @ TA @ ( fun @ TA @ TA ) ) ),E: fun @ nat @ TA] :
( ( dB_rec @ TA @ E @ D @ C @ ( app @ B @ A ) )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( aa @ dB @ ( fun @ TA @ ( fun @ TA @ TA ) ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ TA @ ( fun @ TA @ TA ) ) ) @ D @ B ) @ A ) @ ( dB_rec @ TA @ E @ D @ C @ B ) ) @ ( dB_rec @ TA @ E @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(87,axiom,
( rs
= ( cons @ dB @ a @ as ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_Cons) ).
thf(439,plain,
( rs
= ( cons @ dB @ a @ as ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(69,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
<=> ? [B: TA,C: list @ TA] :
( A
= ( cons @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_neq__Nil__conv) ).
thf(381,plain,
! [TA: $tType,A: list @ TA] :
( ( ( A
!= ( nil @ TA ) )
=> ? [B: TA,C: list @ TA] :
( A
= ( cons @ TA @ B @ C ) ) )
& ( ? [B: TA,C: list @ TA] :
( A
= ( cons @ TA @ B @ C ) )
=> ( A
!= ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(50,axiom,
! [A: nat] :
( ( plus_plus @ nat @ A @ ( zero_zero @ nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_Nat_Oadd__0__right) ).
thf(302,plain,
! [A: nat] :
( ( plus_plus @ nat @ A @ ( zero_zero @ nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(42,axiom,
! [A: nat,B: nat] :
( ( ( plus_plus @ nat @ B @ A )
= ( suc @ ( zero_zero @ nat ) ) )
<=> ( ( ( B
= ( suc @ ( zero_zero @ nat ) ) )
& ( A
= ( zero_zero @ nat ) ) )
| ( ( B
= ( zero_zero @ nat ) )
& ( A
= ( suc @ ( zero_zero @ nat ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_add__is__1) ).
thf(260,plain,
! [A: nat,B: nat] :
( ( ( ( plus_plus @ nat @ B @ A )
= ( suc @ ( zero_zero @ nat ) ) )
=> ( ( ( B
= ( suc @ ( zero_zero @ nat ) ) )
& ( A
= ( zero_zero @ nat ) ) )
| ( ( B
= ( zero_zero @ nat ) )
& ( A
= ( suc @ ( zero_zero @ nat ) ) ) ) ) )
& ( ( ( ( B
= ( suc @ ( zero_zero @ nat ) ) )
& ( A
= ( zero_zero @ nat ) ) )
| ( ( B
= ( zero_zero @ nat ) )
& ( A
= ( suc @ ( zero_zero @ nat ) ) ) ) )
=> ( ( plus_plus @ nat @ B @ A )
= ( suc @ ( zero_zero @ nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(19,axiom,
! [A: nat,B: nat] :
( ( ( suc @ B )
= ( suc @ A ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_Suc__inject) ).
thf(160,plain,
! [A: nat,B: nat] :
( ( ( suc @ B )
= ( suc @ A ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(83,axiom,
! [A: nat,B: dB,C: dB] :
( ( app @ C @ B )
!= ( var @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_dB_Osimps_I5_J) ).
thf(429,plain,
! [A: nat,B: dB,C: dB] :
( ( app @ C @ B )
!= ( var @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(101,axiom,
it @ ua,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_Var_I3_J) ).
thf(484,plain,
it @ ua,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(54,axiom,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
= ( plus_plus @ TA @ C @ ( plus_plus @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(324,plain,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
= ( plus_plus @ TA @ C @ ( plus_plus @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(46,axiom,
ab_semigroup_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oab__semigroup__add) ).
thf(285,plain,
ab_semigroup_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(17,axiom,
! [TA: $tType,A: nat,B: fun @ dB @ ( fun @ TA @ TA ),C: fun @ dB @ ( fun @ dB @ ( fun @ TA @ ( fun @ TA @ TA ) ) ),D: fun @ nat @ TA] :
( ( dB_rec @ TA @ D @ C @ B @ ( var @ A ) )
= ( aa @ nat @ TA @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_dB_Orecs_I1_J) ).
thf(156,plain,
! [TA: $tType,A: nat,B: fun @ dB @ ( fun @ TA @ TA ),C: fun @ dB @ ( fun @ dB @ ( fun @ TA @ ( fun @ TA @ TA ) ) ),D: fun @ nat @ TA] :
( ( dB_rec @ TA @ D @ C @ B @ ( var @ A ) )
= ( aa @ nat @ TA @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(80,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( splice @ TA @ ( cons @ TA @ D @ C ) @ ( cons @ TA @ B @ A ) )
= ( cons @ TA @ D @ ( cons @ TA @ B @ ( splice @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_splice_Osimps_I3_J) ).
thf(420,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( splice @ TA @ ( cons @ TA @ D @ C ) @ ( cons @ TA @ B @ A ) )
= ( cons @ TA @ D @ ( cons @ TA @ B @ ( splice @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(103,axiom,
it @ ( subst @ ( app @ ( lift @ u @ ( zero_zero @ nat ) ) @ ( var @ ( zero_zero @ nat ) ) ) @ ( subst @ a @ u @ i ) @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4__096IT_A_I_Ilift_Au_A0_A_092_060degree_062_AVar_A0_J_091a_091u_Pi_093_P0_093_J_096) ).
thf(488,plain,
it @ ( subst @ ( app @ ( lift @ u @ ( zero_zero @ nat ) ) @ ( var @ ( zero_zero @ nat ) ) ) @ ( subst @ a @ u @ i ) @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(7,axiom,
! [TA: $tType,TB: $tType,A: fun @ TB @ ( fun @ ( list @ TB ) @ TA ),B: TA] :
( ( list_case @ TA @ TB @ B @ A @ ( nil @ TB ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_list_Osimps_I4_J) ).
thf(124,plain,
! [TA: $tType,TB: $tType,A: fun @ TB @ ( fun @ ( list @ TB ) @ TA ),B: TA] :
( ( list_case @ TA @ TB @ B @ A @ ( nil @ TB ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(58,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_add__left__imp__eq) ).
thf(339,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(104,axiom,
! [A: nat] : ( it @ ( var @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_Var__IT) ).
thf(489,plain,
! [A: nat] : ( it @ ( var @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(30,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: TA] :
( ( member1 @ TA @ ( cons @ TA @ C @ B ) @ A )
<=> ( ( C = A )
| ( member1 @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_member__rec_I1_J) ).
thf(212,plain,
! [TA: $tType,A: TA,B: list @ TA,C: TA] :
( ( ( member1 @ TA @ ( cons @ TA @ C @ B ) @ A )
=> ( ( C = A )
| ( member1 @ TA @ B @ A ) ) )
& ( ( ( C = A )
| ( member1 @ TA @ B @ A ) )
=> ( member1 @ TA @ ( cons @ TA @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(78,axiom,
! [A: nat] :
( ( suc @ A )
!= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_nat_Osimps_I3_J) ).
thf(412,plain,
! [A: nat] :
( ( suc @ A )
!= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(44,axiom,
! [A: nat,B: fun @ nat @ bool] :
( ( pp @ ( aa @ nat @ bool @ B @ A ) )
=> ( ! [C: nat] :
( ( pp @ ( aa @ nat @ bool @ B @ ( suc @ C ) ) )
=> ( pp @ ( aa @ nat @ bool @ B @ C ) ) )
=> ( pp @ ( aa @ nat @ bool @ B @ ( zero_zero @ nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_zero__induct) ).
thf(279,plain,
! [A: nat,B: fun @ nat @ bool] :
( ( pp @ ( aa @ nat @ bool @ B @ A ) )
=> ( ! [C: nat] :
( ( pp @ ( aa @ nat @ bool @ B @ ( suc @ C ) ) )
=> ( pp @ ( aa @ nat @ bool @ B @ C ) ) )
=> ( pp @ ( aa @ nat @ bool @ B @ ( zero_zero @ nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(89,axiom,
! [A: nat,B: dB] :
( ( it @ B )
=> ( it @ ( app @ B @ ( var @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_app__Var__IT) ).
thf(444,plain,
! [A: nat,B: dB] :
( ( it @ B )
=> ( it @ ( app @ B @ ( var @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(81,axiom,
! [A: dB,B: dB] :
( ( substn @ B @ A @ ( zero_zero @ nat ) )
= ( subst @ B @ A @ ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_substn__subst__0) ).
thf(423,plain,
! [A: dB,B: dB] :
( ( substn @ B @ A @ ( zero_zero @ nat ) )
= ( subst @ B @ A @ ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(47,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_add__left__cancel) ).
thf(286,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(6,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
= ( nil @ TA ) )
<=> ( null @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_eq__Nil__null) ).
thf(118,plain,
! [TA: $tType,A: list @ TA] :
( ( ( A
= ( nil @ TA ) )
=> ( null @ TA @ A ) )
& ( ( null @ TA @ A )
=> ( A
= ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(72,axiom,
! [TA: $tType,A: nat,B: fun @ dB @ TA,C: fun @ dB @ ( fun @ dB @ TA ),D: fun @ nat @ TA] :
( ( dB_case @ TA @ D @ C @ B @ ( var @ A ) )
= ( aa @ nat @ TA @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_dB_Osimps_I10_J) ).
thf(391,plain,
! [TA: $tType,A: nat,B: fun @ dB @ TA,C: fun @ dB @ ( fun @ dB @ TA ),D: fun @ nat @ TA] :
( ( dB_case @ TA @ D @ C @ B @ ( var @ A ) )
= ( aa @ nat @ TA @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(52,axiom,
! [A: nat,B: dB,C: nat] :
( ( liftn @ ( suc @ C ) @ B @ A )
= ( lift @ ( liftn @ C @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_liftn__lift) ).
thf(313,plain,
! [A: nat,B: dB,C: nat] :
( ( liftn @ ( suc @ C ) @ B @ A )
= ( lift @ ( liftn @ C @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(94,axiom,
! [A: nat,B: dB,C: dB,D: dB] :
( ( subst @ ( app @ D @ C ) @ B @ A )
= ( app @ ( subst @ D @ B @ A ) @ ( subst @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_subst__App) ).
thf(466,plain,
! [A: nat,B: dB,C: dB,D: dB] :
( ( subst @ ( app @ D @ C ) @ B @ A )
= ( app @ ( subst @ D @ B @ A ) @ ( subst @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(57,axiom,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_Zero__not__Suc) ).
thf(335,plain,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(18,axiom,
comm_monoid_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocomm__monoid__add) ).
thf(159,plain,
comm_monoid_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(26,axiom,
! [A: nat,B: nat] :
( ( ( suc @ ( zero_zero @ nat ) )
= ( plus_plus @ nat @ B @ A ) )
<=> ( ( ( B
= ( suc @ ( zero_zero @ nat ) ) )
& ( A
= ( zero_zero @ nat ) ) )
| ( ( B
= ( zero_zero @ nat ) )
& ( A
= ( suc @ ( zero_zero @ nat ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_one__is__add) ).
thf(187,plain,
! [A: nat,B: nat] :
( ( ( ( suc @ ( zero_zero @ nat ) )
= ( plus_plus @ nat @ B @ A ) )
=> ( ( ( B
= ( suc @ ( zero_zero @ nat ) ) )
& ( A
= ( zero_zero @ nat ) ) )
| ( ( B
= ( zero_zero @ nat ) )
& ( A
= ( suc @ ( zero_zero @ nat ) ) ) ) ) )
& ( ( ( ( B
= ( suc @ ( zero_zero @ nat ) ) )
& ( A
= ( zero_zero @ nat ) ) )
| ( ( B
= ( zero_zero @ nat ) )
& ( A
= ( suc @ ( zero_zero @ nat ) ) ) ) )
=> ( ( suc @ ( zero_zero @ nat ) )
= ( plus_plus @ nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(4,axiom,
! [TA: $tType,A: list @ TA] :
( ( splice @ TA @ A @ ( nil @ TA ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_splice__Nil2) ).
thf(113,plain,
! [TA: $tType,A: list @ TA] :
( ( splice @ TA @ A @ ( nil @ TA ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(31,axiom,
! [A: nat,B: nat] :
( ( ( var @ B )
= ( var @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_dB_Osimps_I1_J) ).
thf(219,plain,
! [A: nat,B: nat] :
( ( ( ( var @ B )
= ( var @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( var @ B )
= ( var @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(68,axiom,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_nat_Osimps_I2_J) ).
thf(377,plain,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(33,axiom,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_Zero__neq__Suc) ).
thf(230,plain,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(37,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
~ ( null @ TA @ ( cons @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_null__rec_I1_J) ).
thf(245,plain,
! [TA: $tType,A: list @ TA,B: TA] :
~ ( null @ TA @ ( cons @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(99,axiom,
! [A: nat,B: dB,C: dB] :
( ( substn @ C @ B @ A )
= ( subst @ C @ ( liftn @ A @ B @ ( zero_zero @ nat ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_substn__subst__n) ).
thf(477,plain,
! [A: nat,B: dB,C: dB] :
( ( substn @ C @ B @ A )
= ( subst @ C @ ( liftn @ A @ B @ ( zero_zero @ nat ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(70,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_list_Oexhaust) ).
thf(387,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(56,axiom,
! [TA: $tType,A: TA,B: fun @ nat @ bool] :
( ( ( member @ nat @ ( zero_zero @ nat ) @ B )
=> ( ( sublist @ TA @ ( cons @ TA @ A @ ( nil @ TA ) ) @ B )
= ( cons @ TA @ A @ ( nil @ TA ) ) ) )
& ( ~ ( member @ nat @ ( zero_zero @ nat ) @ B )
=> ( ( sublist @ TA @ ( cons @ TA @ A @ ( nil @ TA ) ) @ B )
= ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_sublist__singleton) ).
thf(330,plain,
! [TA: $tType,A: TA,B: fun @ nat @ bool] :
( ( ( member @ nat @ ( zero_zero @ nat ) @ B )
=> ( ( sublist @ TA @ ( cons @ TA @ A @ ( nil @ TA ) ) @ B )
= ( cons @ TA @ A @ ( nil @ TA ) ) ) )
& ( ~ ( member @ nat @ ( zero_zero @ nat ) @ B )
=> ( ( sublist @ TA @ ( cons @ TA @ A @ ( nil @ TA ) ) @ B )
= ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(60,axiom,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA,C: fun @ TA @ ( fun @ ( list @ TA ) @ TB ),D: TB] :
( ( list_case @ TB @ TA @ D @ C @ ( cons @ TA @ B @ A ) )
= ( aa @ ( list @ TA ) @ TB @ ( aa @ TA @ ( fun @ ( list @ TA ) @ TB ) @ C @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_list_Osimps_I5_J) ).
thf(345,plain,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA,C: fun @ TA @ ( fun @ ( list @ TA ) @ TB ),D: TB] :
( ( list_case @ TB @ TA @ D @ C @ ( cons @ TA @ B @ A ) )
= ( aa @ ( list @ TA ) @ TB @ ( aa @ TA @ ( fun @ ( list @ TA ) @ TB ) @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(65,axiom,
! [TA: $tType,A: list @ TA,B: TA] : ( listMem @ TA @ B @ ( cons @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_elem) ).
thf(367,plain,
! [TA: $tType,A: list @ TA,B: TA] : ( listMem @ TA @ B @ ( cons @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(9,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( splice @ TA @ ( cons @ TA @ B @ A ) @ ( nil @ TA ) )
= ( cons @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_splice_Osimps_I2_J) ).
thf(130,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( splice @ TA @ ( cons @ TA @ B @ A ) @ ( nil @ TA ) )
= ( cons @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(93,axiom,
! [A: dB,B: dB,C: dB,D: dB] :
( ( ( app @ D @ C )
= ( app @ B @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_dB_Osimps_I2_J) ).
thf(455,plain,
! [A: dB,B: dB,C: dB,D: dB] :
( ( ( ( app @ D @ C )
= ( app @ B @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( app @ D @ C )
= ( app @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(73,axiom,
! [A: nat,B: dB] :
( ( liftn @ ( zero_zero @ nat ) @ B @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_liftn__0) ).
thf(394,plain,
! [A: nat,B: dB] :
( ( liftn @ ( zero_zero @ nat ) @ B @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(36,axiom,
! [A: nat] :
( A
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_n__not__Suc__n) ).
thf(241,plain,
! [A: nat] :
( A
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(82,axiom,
! [A: dB,B: nat] :
( ( subst @ ( var @ B ) @ A @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_subst__eq) ).
thf(426,plain,
! [A: dB,B: nat] :
( ( subst @ ( var @ B ) @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(29,axiom,
! [A: nat,B: fun @ nat @ bool] :
( ( pp @ ( aa @ nat @ bool @ B @ ( zero_zero @ nat ) ) )
=> ( ! [C: nat] :
( ( pp @ ( aa @ nat @ bool @ B @ C ) )
=> ( pp @ ( aa @ nat @ bool @ B @ ( suc @ C ) ) ) )
=> ( pp @ ( aa @ nat @ bool @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_nat__induct) ).
thf(209,plain,
! [A: nat,B: fun @ nat @ bool] :
( ( pp @ ( aa @ nat @ bool @ B @ ( zero_zero @ nat ) ) )
=> ( ! [C: nat] :
( ( pp @ ( aa @ nat @ bool @ B @ C ) )
=> ( pp @ ( aa @ nat @ bool @ B @ ( suc @ C ) ) ) )
=> ( pp @ ( aa @ nat @ bool @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(59,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( cons @ TA @ B @ A )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_not__Cons__self2) ).
thf(342,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( cons @ TA @ B @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(62,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ A @ B ) )
=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_add__right__imp__eq) ).
thf(355,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ A @ B ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(13,axiom,
! [TA: $tType,A: TA] :
~ ( member1 @ TA @ ( nil @ TA ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_member__rec_I2_J) ).
thf(145,plain,
! [TA: $tType,A: TA] :
~ ( member1 @ TA @ ( nil @ TA ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(49,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ C @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_nat__add__left__cancel) ).
thf(295,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ C @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(45,axiom,
! [A: nat] :
( ( dB_size @ ( var @ A ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_dB_Osize_I1_J) ).
thf(282,plain,
! [A: nat] :
( ( dB_size @ ( var @ A ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(15,axiom,
! [TA: $tType,TB: $tType,A: fun @ TB @ ( fun @ ( list @ TB ) @ ( fun @ TA @ TA ) ),B: TA] :
( ( list_rec @ TA @ TB @ B @ A @ ( nil @ TB ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_list_Orecs_I1_J) ).
thf(150,plain,
! [TA: $tType,TB: $tType,A: fun @ TB @ ( fun @ ( list @ TB ) @ ( fun @ TA @ TA ) ),B: TA] :
( ( list_rec @ TA @ TB @ B @ A @ ( nil @ TB ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(55,axiom,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ ( suc @ B ) @ A )
= ( plus_plus @ nat @ B @ ( suc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_add__Suc__shift) ).
thf(327,plain,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ ( suc @ B ) @ A )
= ( plus_plus @ nat @ B @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(88,axiom,
! [A: nat,B: dB,C: dB,D: dB] :
( ( substn @ ( app @ D @ C ) @ B @ A )
= ( app @ ( substn @ D @ B @ A ) @ ( substn @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_substn_Osimps_I2_J) ).
thf(441,plain,
! [A: nat,B: dB,C: dB,D: dB] :
( ( substn @ ( app @ D @ C ) @ B @ A )
= ( app @ ( substn @ D @ B @ A ) @ ( substn @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(8,axiom,
! [TA: $tType,A: fun @ nat @ bool] :
( ( sublist @ TA @ ( nil @ TA ) @ A )
= ( nil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_sublist__nil) ).
thf(127,plain,
! [TA: $tType,A: fun @ nat @ bool] :
( ( sublist @ TA @ ( nil @ TA ) @ A )
= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(96,axiom,
! [A: nat,B: nat,C: dB] :
( ( it @ C )
=> ( it @ ( subst @ C @ ( var @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_subst__Var__IT) ).
thf(470,plain,
! [A: nat,B: nat,C: dB] :
( ( it @ C )
=> ( it @ ( subst @ C @ ( var @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(39,axiom,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ B @ ( suc @ A ) )
= ( suc @ ( plus_plus @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_add__Suc__right) ).
thf(250,plain,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ B @ ( suc @ A ) )
= ( suc @ ( plus_plus @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(27,axiom,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ B @ A )
= ( plus_plus @ nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_nat__add__commute) ).
thf(203,plain,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ B @ A )
= ( plus_plus @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(71,axiom,
cancel146912293up_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) ).
thf(390,plain,
cancel146912293up_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(22,axiom,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA,C: fun @ TA @ ( fun @ ( list @ TA ) @ ( fun @ TB @ TB ) ),D: TB] :
( ( list_rec @ TB @ TA @ D @ C @ ( cons @ TA @ B @ A ) )
= ( aa @ TB @ TB @ ( aa @ ( list @ TA ) @ ( fun @ TB @ TB ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( fun @ TB @ TB ) ) @ C @ B ) @ A ) @ ( list_rec @ TB @ TA @ D @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_list_Orecs_I2_J) ).
thf(171,plain,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA,C: fun @ TA @ ( fun @ ( list @ TA ) @ ( fun @ TB @ TB ) ),D: TB] :
( ( list_rec @ TB @ TA @ D @ C @ ( cons @ TA @ B @ A ) )
= ( aa @ TB @ TB @ ( aa @ ( list @ TA ) @ ( fun @ TB @ TB ) @ ( aa @ TA @ ( fun @ ( list @ TA ) @ ( fun @ TB @ TB ) ) @ C @ B ) @ A ) @ ( list_rec @ TB @ TA @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(11,axiom,
! [TA: $tType,A: list @ TA] :
( ( splice @ TA @ ( nil @ TA ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_splice_Osimps_I1_J) ).
thf(139,plain,
! [TA: $tType,A: list @ TA] :
( ( splice @ TA @ ( nil @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(21,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus @ nat @ C @ ( plus_plus @ nat @ B @ A ) )
= ( plus_plus @ nat @ B @ ( plus_plus @ nat @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_nat__add__left__commute) ).
thf(168,plain,
! [A: nat,B: nat,C: nat] :
( ( plus_plus @ nat @ C @ ( plus_plus @ nat @ B @ A ) )
= ( plus_plus @ nat @ B @ ( plus_plus @ nat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(24,axiom,
zero @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
thf(183,plain,
zero @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(51,axiom,
! [A: nat,B: nat] :
( ( ( suc @ B )
= ( suc @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_nat_Oinject) ).
thf(305,plain,
! [A: nat,B: nat] :
( ( ( ( suc @ B )
= ( suc @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( suc @ B )
= ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(3,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( equal_equal @ ( list @ TA ) @ B @ A )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_equal__list__def) ).
thf(107,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( equal_equal @ ( list @ TA ) @ B @ A )
=> ( B = A ) )
& ( ( B = A )
=> ( equal_equal @ ( list @ TA ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(63,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ A ) )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_double__zero__sym) ).
thf(358,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ A ) )
=> ( A
= ( zero_zero @ TA ) ) )
& ( ( A
= ( zero_zero @ TA ) )
=> ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(86,axiom,
! [A: nat,B: dB] :
( ( it @ B )
=> ( it @ ( lift @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_lift__IT) ).
thf(437,plain,
! [A: nat,B: dB] :
( ( it @ B )
=> ( it @ ( lift @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(75,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ~ ! [B: nat] :
( A
!= ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_nat_Oexhaust) ).
thf(400,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ~ ! [B: nat] :
( A
!= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(32,axiom,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_add__imp__eq) ).
thf(227,plain,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(95,axiom,
it @ u,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_uIT) ).
thf(469,plain,
it @ u,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(105,axiom,
! [A: dB,B: nat,C: dB] :
( ( subst @ ( lift @ C @ B ) @ A @ B )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_subst__lift) ).
thf(491,plain,
! [A: dB,B: nat,C: dB] :
( ( subst @ ( lift @ C @ B ) @ A @ B )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(64,axiom,
! [TA: $tType,A: TA] :
( ( insert @ TA @ A @ ( nil @ TA ) )
= ( cons @ TA @ A @ ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_insert__Nil) ).
thf(364,plain,
! [TA: $tType,A: TA] :
( ( insert @ TA @ A @ ( nil @ TA ) )
= ( cons @ TA @ A @ ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(494,plain,
$false,
inference(e,[status(thm)],[234,184,371,446,433,369,276,449,247,142,472,153,436,257,174,404,416,316,475,164,253,485,106,238,348,480,147,397,133,411,116,206,292,452,439,381,302,260,160,429,484,324,285,156,420,488,124,339,489,212,412,279,444,423,286,118,391,313,466,335,159,187,113,219,377,230,245,477,387,330,345,367,130,455,394,241,426,209,342,355,145,295,282,150,327,441,127,470,250,203,390,171,139,168,183,305,107,358,437,400,227,469,491,364]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : LCL800_5 : TPTP v8.1.2. Released v6.0.0.
% 0.06/0.14 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n006.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu May 18 15:55:22 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.95/0.88 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.56/1.07 % [INFO] Parsing done (192ms).
% 1.56/1.08 % [INFO] Running in sequential loop mode.
% 2.00/1.26 % [INFO] eprover registered as external prover.
% 2.00/1.27 % [INFO] cvc4 registered as external prover.
% 2.00/1.27 % [INFO] Scanning for conjecture ...
% 2.20/1.35 % [INFO] Found a conjecture and 105 axioms. Running axiom selection ...
% 2.31/1.42 % [INFO] Axiom selection finished. Selected 103 axioms (removed 2 axioms).
% 2.81/1.54 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.81/1.56 % [INFO] Type checking passed.
% 2.92/1.56 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 6.21/2.46 % External prover 'e' found a proof!
% 6.21/2.46 % [INFO] Killing All external provers ...
% 6.21/2.46 % Time passed: 1954ms (effective reasoning time: 1381ms)
% 6.21/2.46 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 6.21/2.46 % Axioms used in derivation (103): fact_93_ab__semigroup__add__class_Oadd__ac_I1_J, fact_37_liftn__lift, fact_75_add__right__cancel, fact_22_dB_Osimps_I10_J, fact_74_add__left__cancel, fact_33_null__rec_I1_J, fact_43_list_Osimps_I2_J, fact_54_neq__Nil__conv, fact_84_add__is__1, fact_11_lift_Osimps_I2_J, fact_71_dB_Osize_I2_J, fact_20_dB_Osize_I4_J, fact_24_substn_Osimps_I2_J, fact_67_nat_Oexhaust, fact_28_substn__subst__n, fact_8_app__Var__IT, fact_85_add__Suc__shift, fact_2_uIT, fact_62_nat_Osimps_I3_J, fact_48_splice_Osimps_I1_J, fact_92_equal__list__def, fact_4__096IT_A_I_Ilift_Au_A0_A_092_060degree_062_AVar_A0_J_091a_091u_Pi_093_P0_093_J_096, fact_73_mem__def, fact_56_n__not__Suc__n, fact_31_list_Orecs_I2_J, fact_36_dB_Orecs_I2_J, fact_14_subst__eq, fact_0__096IT_At_096, fact_44_list_Osimps_I3_J, arity_Nat_Onat___Groups_Ocomm__monoid__add, fact_89_nat__add__commute, fact_83_one__is__add, fact_78_double__zero__sym, fact_90_nat__add__left__commute, fact_9_dB_Osimps_I2_J, fact_3_True, fact_96_add__right__imp__eq, fact_50_eq__Nil__null, fact_94_add__left__imp__eq, fact_13_subst__lift, fact_61_Suc__not__Zero, fact_81_add__Suc__right, fact_87_Nat_Oadd__0__right, fact_30_splice_Osimps_I3_J, fact_77_nat__add__right__cancel, fact_60_nat_Osimps_I2_J, fact_88_add__eq__self__zero, fact_65_nat__induct, fact_63_Zero__neq__Suc, fact_82_dB_Osize_I5_J, fact_68_insert__Nil, fact_18_list_Oinject, fact_1_Var_I3_J, fact_52_nat_Oinject, fact_55_Suc__neq__Zero, fact_58_Suc__inject, fact_15_dB_Osimps_I4_J, fact_72_equal__Nil__null, fact_25_zero__reorient, fact_53_list_Oexhaust, fact_35_liftn__0, fact_7_subst__Var__IT, fact_19_dB_Osize_I1_J, fact_38_elem, arity_Nat_Onat___Groups_Ozero, fact_16_dB_Osimps_I5_J, fact_46_null__rec_I2_J, fact_86_plus__nat_Oadd__0, fact_12_Cons, fact_27_not__Cons__self, fact_49_splice__Nil2, fact_6_subst__App, fact_51_list_Orecs_I1_J, fact_23_dB_Osimps_I11_J, fact_80_add__Suc, fact_42_member__rec_I2_J, fact_32_liftn_Osimps_I2_J, fact_26_not__Cons__self2, fact_40_insert, fact_69_sublist__singleton, fact_21_substn__subst__0, fact_34_dB_Orecs_I1_J, fact_5_lift__IT, fact_79_add__is__0, fact_10_Var__IT, fact_29_list_Osimps_I5_J, fact_59_Zero__not__Suc, fact_76_nat__add__left__cancel, fact_95_add__imp__eq, arity_Nat_Onat___Groups_Oab__semigroup__add, fact_39_member__rec_I1_J, arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add, fact_91_nat__add__assoc, fact_64_not0__implies__Suc, fact_41_splice_Osimps_I2_J, fact_97_add_Ocomm__neutral, fact_66_zero__induct, fact_57_Suc__n__not__n, arity_Nat_Onat___Groups_Ocancel__semigroup__add, fact_47_List_Onull__def, fact_45_list_Osimps_I4_J, fact_17_dB_Osimps_I1_J, fact_70_sublist__nil
% 6.21/2.46 % No. of inferences in proof: 210
% 6.21/2.46 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1954 ms resp. 1381 ms w/o parsing
% 6.21/2.53 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.21/2.53 % [INFO] Killing All external provers ...
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